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<FONT color="green">001</FONT>    /*<a name="line.1"></a>
<FONT color="green">002</FONT>     * Licensed to the Apache Software Foundation (ASF) under one or more<a name="line.2"></a>
<FONT color="green">003</FONT>     * contributor license agreements.  See the NOTICE file distributed with<a name="line.3"></a>
<FONT color="green">004</FONT>     * this work for additional information regarding copyright ownership.<a name="line.4"></a>
<FONT color="green">005</FONT>     * The ASF licenses this file to You under the Apache License, Version 2.0<a name="line.5"></a>
<FONT color="green">006</FONT>     * (the "License"); you may not use this file except in compliance with<a name="line.6"></a>
<FONT color="green">007</FONT>     * the License.  You may obtain a copy of the License at<a name="line.7"></a>
<FONT color="green">008</FONT>     *<a name="line.8"></a>
<FONT color="green">009</FONT>     *      http://www.apache.org/licenses/LICENSE-2.0<a name="line.9"></a>
<FONT color="green">010</FONT>     *<a name="line.10"></a>
<FONT color="green">011</FONT>     * Unless required by applicable law or agreed to in writing, software<a name="line.11"></a>
<FONT color="green">012</FONT>     * distributed under the License is distributed on an "AS IS" BASIS,<a name="line.12"></a>
<FONT color="green">013</FONT>     * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.<a name="line.13"></a>
<FONT color="green">014</FONT>     * See the License for the specific language governing permissions and<a name="line.14"></a>
<FONT color="green">015</FONT>     * limitations under the License.<a name="line.15"></a>
<FONT color="green">016</FONT>     */<a name="line.16"></a>
<FONT color="green">017</FONT>    <a name="line.17"></a>
<FONT color="green">018</FONT>    package org.apache.commons.math3.analysis.function;<a name="line.18"></a>
<FONT color="green">019</FONT>    <a name="line.19"></a>
<FONT color="green">020</FONT>    import org.apache.commons.math3.analysis.DifferentiableUnivariateFunction;<a name="line.20"></a>
<FONT color="green">021</FONT>    import org.apache.commons.math3.analysis.FunctionUtils;<a name="line.21"></a>
<FONT color="green">022</FONT>    import org.apache.commons.math3.analysis.ParametricUnivariateFunction;<a name="line.22"></a>
<FONT color="green">023</FONT>    import org.apache.commons.math3.analysis.UnivariateFunction;<a name="line.23"></a>
<FONT color="green">024</FONT>    import org.apache.commons.math3.analysis.differentiation.DerivativeStructure;<a name="line.24"></a>
<FONT color="green">025</FONT>    import org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction;<a name="line.25"></a>
<FONT color="green">026</FONT>    import org.apache.commons.math3.exception.DimensionMismatchException;<a name="line.26"></a>
<FONT color="green">027</FONT>    import org.apache.commons.math3.exception.NullArgumentException;<a name="line.27"></a>
<FONT color="green">028</FONT>    import org.apache.commons.math3.util.FastMath;<a name="line.28"></a>
<FONT color="green">029</FONT>    <a name="line.29"></a>
<FONT color="green">030</FONT>    /**<a name="line.30"></a>
<FONT color="green">031</FONT>     * &lt;a href="http://en.wikipedia.org/wiki/Harmonic_oscillator"&gt;<a name="line.31"></a>
<FONT color="green">032</FONT>     *  simple harmonic oscillator&lt;/a&gt; function.<a name="line.32"></a>
<FONT color="green">033</FONT>     *<a name="line.33"></a>
<FONT color="green">034</FONT>     * @since 3.0<a name="line.34"></a>
<FONT color="green">035</FONT>     * @version $Id: HarmonicOscillator.java 1383441 2012-09-11 14:56:39Z luc $<a name="line.35"></a>
<FONT color="green">036</FONT>     */<a name="line.36"></a>
<FONT color="green">037</FONT>    public class HarmonicOscillator implements UnivariateDifferentiableFunction, DifferentiableUnivariateFunction {<a name="line.37"></a>
<FONT color="green">038</FONT>        /** Amplitude. */<a name="line.38"></a>
<FONT color="green">039</FONT>        private final double amplitude;<a name="line.39"></a>
<FONT color="green">040</FONT>        /** Angular frequency. */<a name="line.40"></a>
<FONT color="green">041</FONT>        private final double omega;<a name="line.41"></a>
<FONT color="green">042</FONT>        /** Phase. */<a name="line.42"></a>
<FONT color="green">043</FONT>        private final double phase;<a name="line.43"></a>
<FONT color="green">044</FONT>    <a name="line.44"></a>
<FONT color="green">045</FONT>        /**<a name="line.45"></a>
<FONT color="green">046</FONT>         * Harmonic oscillator function.<a name="line.46"></a>
<FONT color="green">047</FONT>         *<a name="line.47"></a>
<FONT color="green">048</FONT>         * @param amplitude Amplitude.<a name="line.48"></a>
<FONT color="green">049</FONT>         * @param omega Angular frequency.<a name="line.49"></a>
<FONT color="green">050</FONT>         * @param phase Phase.<a name="line.50"></a>
<FONT color="green">051</FONT>         */<a name="line.51"></a>
<FONT color="green">052</FONT>        public HarmonicOscillator(double amplitude,<a name="line.52"></a>
<FONT color="green">053</FONT>                                  double omega,<a name="line.53"></a>
<FONT color="green">054</FONT>                                  double phase) {<a name="line.54"></a>
<FONT color="green">055</FONT>            this.amplitude = amplitude;<a name="line.55"></a>
<FONT color="green">056</FONT>            this.omega = omega;<a name="line.56"></a>
<FONT color="green">057</FONT>            this.phase = phase;<a name="line.57"></a>
<FONT color="green">058</FONT>        }<a name="line.58"></a>
<FONT color="green">059</FONT>    <a name="line.59"></a>
<FONT color="green">060</FONT>        /** {@inheritDoc} */<a name="line.60"></a>
<FONT color="green">061</FONT>        public double value(double x) {<a name="line.61"></a>
<FONT color="green">062</FONT>            return value(omega * x + phase, amplitude);<a name="line.62"></a>
<FONT color="green">063</FONT>        }<a name="line.63"></a>
<FONT color="green">064</FONT>    <a name="line.64"></a>
<FONT color="green">065</FONT>        /** {@inheritDoc}<a name="line.65"></a>
<FONT color="green">066</FONT>         * @deprecated as of 3.1, replaced by {@link #value(DerivativeStructure)}<a name="line.66"></a>
<FONT color="green">067</FONT>         */<a name="line.67"></a>
<FONT color="green">068</FONT>        @Deprecated<a name="line.68"></a>
<FONT color="green">069</FONT>        public UnivariateFunction derivative() {<a name="line.69"></a>
<FONT color="green">070</FONT>            return FunctionUtils.toDifferentiableUnivariateFunction(this).derivative();<a name="line.70"></a>
<FONT color="green">071</FONT>        }<a name="line.71"></a>
<FONT color="green">072</FONT>    <a name="line.72"></a>
<FONT color="green">073</FONT>        /**<a name="line.73"></a>
<FONT color="green">074</FONT>         * Parametric function where the input array contains the parameters of<a name="line.74"></a>
<FONT color="green">075</FONT>         * the harmonic oscillator function, ordered as follows:<a name="line.75"></a>
<FONT color="green">076</FONT>         * &lt;ul&gt;<a name="line.76"></a>
<FONT color="green">077</FONT>         *  &lt;li&gt;Amplitude&lt;/li&gt;<a name="line.77"></a>
<FONT color="green">078</FONT>         *  &lt;li&gt;Angular frequency&lt;/li&gt;<a name="line.78"></a>
<FONT color="green">079</FONT>         *  &lt;li&gt;Phase&lt;/li&gt;<a name="line.79"></a>
<FONT color="green">080</FONT>         * &lt;/ul&gt;<a name="line.80"></a>
<FONT color="green">081</FONT>         */<a name="line.81"></a>
<FONT color="green">082</FONT>        public static class Parametric implements ParametricUnivariateFunction {<a name="line.82"></a>
<FONT color="green">083</FONT>            /**<a name="line.83"></a>
<FONT color="green">084</FONT>             * Computes the value of the harmonic oscillator at {@code x}.<a name="line.84"></a>
<FONT color="green">085</FONT>             *<a name="line.85"></a>
<FONT color="green">086</FONT>             * @param x Value for which the function must be computed.<a name="line.86"></a>
<FONT color="green">087</FONT>             * @param param Values of norm, mean and standard deviation.<a name="line.87"></a>
<FONT color="green">088</FONT>             * @return the value of the function.<a name="line.88"></a>
<FONT color="green">089</FONT>             * @throws NullArgumentException if {@code param} is {@code null}.<a name="line.89"></a>
<FONT color="green">090</FONT>             * @throws DimensionMismatchException if the size of {@code param} is<a name="line.90"></a>
<FONT color="green">091</FONT>             * not 3.<a name="line.91"></a>
<FONT color="green">092</FONT>             */<a name="line.92"></a>
<FONT color="green">093</FONT>            public double value(double x, double ... param)<a name="line.93"></a>
<FONT color="green">094</FONT>                throws NullArgumentException,<a name="line.94"></a>
<FONT color="green">095</FONT>                       DimensionMismatchException {<a name="line.95"></a>
<FONT color="green">096</FONT>                validateParameters(param);<a name="line.96"></a>
<FONT color="green">097</FONT>                return HarmonicOscillator.value(x * param[1] + param[2], param[0]);<a name="line.97"></a>
<FONT color="green">098</FONT>            }<a name="line.98"></a>
<FONT color="green">099</FONT>    <a name="line.99"></a>
<FONT color="green">100</FONT>            /**<a name="line.100"></a>
<FONT color="green">101</FONT>             * Computes the value of the gradient at {@code x}.<a name="line.101"></a>
<FONT color="green">102</FONT>             * The components of the gradient vector are the partial<a name="line.102"></a>
<FONT color="green">103</FONT>             * derivatives of the function with respect to each of the<a name="line.103"></a>
<FONT color="green">104</FONT>             * &lt;em&gt;parameters&lt;/em&gt; (amplitude, angular frequency and phase).<a name="line.104"></a>
<FONT color="green">105</FONT>             *<a name="line.105"></a>
<FONT color="green">106</FONT>             * @param x Value at which the gradient must be computed.<a name="line.106"></a>
<FONT color="green">107</FONT>             * @param param Values of amplitude, angular frequency and phase.<a name="line.107"></a>
<FONT color="green">108</FONT>             * @return the gradient vector at {@code x}.<a name="line.108"></a>
<FONT color="green">109</FONT>             * @throws NullArgumentException if {@code param} is {@code null}.<a name="line.109"></a>
<FONT color="green">110</FONT>             * @throws DimensionMismatchException if the size of {@code param} is<a name="line.110"></a>
<FONT color="green">111</FONT>             * not 3.<a name="line.111"></a>
<FONT color="green">112</FONT>             */<a name="line.112"></a>
<FONT color="green">113</FONT>            public double[] gradient(double x, double ... param)<a name="line.113"></a>
<FONT color="green">114</FONT>                throws NullArgumentException,<a name="line.114"></a>
<FONT color="green">115</FONT>                       DimensionMismatchException {<a name="line.115"></a>
<FONT color="green">116</FONT>                validateParameters(param);<a name="line.116"></a>
<FONT color="green">117</FONT>    <a name="line.117"></a>
<FONT color="green">118</FONT>                final double amplitude = param[0];<a name="line.118"></a>
<FONT color="green">119</FONT>                final double omega = param[1];<a name="line.119"></a>
<FONT color="green">120</FONT>                final double phase = param[2];<a name="line.120"></a>
<FONT color="green">121</FONT>    <a name="line.121"></a>
<FONT color="green">122</FONT>                final double xTimesOmegaPlusPhase = omega * x + phase;<a name="line.122"></a>
<FONT color="green">123</FONT>                final double a = HarmonicOscillator.value(xTimesOmegaPlusPhase, 1);<a name="line.123"></a>
<FONT color="green">124</FONT>                final double p = -amplitude * FastMath.sin(xTimesOmegaPlusPhase);<a name="line.124"></a>
<FONT color="green">125</FONT>                final double w = p * x;<a name="line.125"></a>
<FONT color="green">126</FONT>    <a name="line.126"></a>
<FONT color="green">127</FONT>                return new double[] { a, w, p };<a name="line.127"></a>
<FONT color="green">128</FONT>            }<a name="line.128"></a>
<FONT color="green">129</FONT>    <a name="line.129"></a>
<FONT color="green">130</FONT>            /**<a name="line.130"></a>
<FONT color="green">131</FONT>             * Validates parameters to ensure they are appropriate for the evaluation of<a name="line.131"></a>
<FONT color="green">132</FONT>             * the {@link #value(double,double[])} and {@link #gradient(double,double[])}<a name="line.132"></a>
<FONT color="green">133</FONT>             * methods.<a name="line.133"></a>
<FONT color="green">134</FONT>             *<a name="line.134"></a>
<FONT color="green">135</FONT>             * @param param Values of norm, mean and standard deviation.<a name="line.135"></a>
<FONT color="green">136</FONT>             * @throws NullArgumentException if {@code param} is {@code null}.<a name="line.136"></a>
<FONT color="green">137</FONT>             * @throws DimensionMismatchException if the size of {@code param} is<a name="line.137"></a>
<FONT color="green">138</FONT>             * not 3.<a name="line.138"></a>
<FONT color="green">139</FONT>             */<a name="line.139"></a>
<FONT color="green">140</FONT>            private void validateParameters(double[] param)<a name="line.140"></a>
<FONT color="green">141</FONT>                throws NullArgumentException,<a name="line.141"></a>
<FONT color="green">142</FONT>                       DimensionMismatchException {<a name="line.142"></a>
<FONT color="green">143</FONT>                if (param == null) {<a name="line.143"></a>
<FONT color="green">144</FONT>                    throw new NullArgumentException();<a name="line.144"></a>
<FONT color="green">145</FONT>                }<a name="line.145"></a>
<FONT color="green">146</FONT>                if (param.length != 3) {<a name="line.146"></a>
<FONT color="green">147</FONT>                    throw new DimensionMismatchException(param.length, 3);<a name="line.147"></a>
<FONT color="green">148</FONT>                }<a name="line.148"></a>
<FONT color="green">149</FONT>            }<a name="line.149"></a>
<FONT color="green">150</FONT>        }<a name="line.150"></a>
<FONT color="green">151</FONT>    <a name="line.151"></a>
<FONT color="green">152</FONT>        /**<a name="line.152"></a>
<FONT color="green">153</FONT>         * @param xTimesOmegaPlusPhase {@code omega * x + phase}.<a name="line.153"></a>
<FONT color="green">154</FONT>         * @param amplitude Amplitude.<a name="line.154"></a>
<FONT color="green">155</FONT>         * @return the value of the harmonic oscillator function at {@code x}.<a name="line.155"></a>
<FONT color="green">156</FONT>         */<a name="line.156"></a>
<FONT color="green">157</FONT>        private static double value(double xTimesOmegaPlusPhase,<a name="line.157"></a>
<FONT color="green">158</FONT>                                    double amplitude) {<a name="line.158"></a>
<FONT color="green">159</FONT>            return amplitude * FastMath.cos(xTimesOmegaPlusPhase);<a name="line.159"></a>
<FONT color="green">160</FONT>        }<a name="line.160"></a>
<FONT color="green">161</FONT>    <a name="line.161"></a>
<FONT color="green">162</FONT>        /** {@inheritDoc}<a name="line.162"></a>
<FONT color="green">163</FONT>         * @since 3.1<a name="line.163"></a>
<FONT color="green">164</FONT>         */<a name="line.164"></a>
<FONT color="green">165</FONT>        public DerivativeStructure value(final DerivativeStructure t) {<a name="line.165"></a>
<FONT color="green">166</FONT>            final double x = t.getValue();<a name="line.166"></a>
<FONT color="green">167</FONT>            double[] f = new double[t.getOrder() + 1];<a name="line.167"></a>
<FONT color="green">168</FONT>    <a name="line.168"></a>
<FONT color="green">169</FONT>            final double alpha = omega * x + phase;<a name="line.169"></a>
<FONT color="green">170</FONT>            f[0] = amplitude * FastMath.cos(alpha);<a name="line.170"></a>
<FONT color="green">171</FONT>            if (f.length &gt; 1) {<a name="line.171"></a>
<FONT color="green">172</FONT>                f[1] = -amplitude * omega * FastMath.sin(alpha);<a name="line.172"></a>
<FONT color="green">173</FONT>                final double mo2 = - omega * omega;<a name="line.173"></a>
<FONT color="green">174</FONT>                for (int i = 2; i &lt; f.length; ++i) {<a name="line.174"></a>
<FONT color="green">175</FONT>                    f[i] = mo2 * f[i - 2];<a name="line.175"></a>
<FONT color="green">176</FONT>                }<a name="line.176"></a>
<FONT color="green">177</FONT>            }<a name="line.177"></a>
<FONT color="green">178</FONT>    <a name="line.178"></a>
<FONT color="green">179</FONT>            return t.compose(f);<a name="line.179"></a>
<FONT color="green">180</FONT>    <a name="line.180"></a>
<FONT color="green">181</FONT>        }<a name="line.181"></a>
<FONT color="green">182</FONT>    <a name="line.182"></a>
<FONT color="green">183</FONT>    }<a name="line.183"></a>




























































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